Anova 1 Way - Fixed Model - General Linear Models



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Report - Anova 1 Way - Fixed Model - General Linear Models

1) Anova test

test aim variable p_value alpha_value Decision
Shapiro-Wilk test Normality residuals 0.5176650 0.05 Ho no rejected
Bartlett test Homogeneity residuals 0.0150452 0.05 Ho Rejected
Anova 1 way Mean mpg 0.0000000 0.05 Ho Rejected

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The null hypothesis of normal distribution of residuals is not rejected.
The hypothesis of homogeneity of variances (homoscedasticity) is rejected.
Not all model assumptions are met, so it is NOT valid to draw conclusions from the ANOVA test.
Regardless of the p-value obtained in ANOVA, it is not valid to draw conclusions.

1) References

$df_selected_vars
  order var_name var_number var_letter var_role doble_reference
1     1      mpg          1          A       VR         VR(mpg)
2     2      cyl          2          B   FACTOR     FACTOR(cyl)

2) Summary Factor

$df_factor_info
  order level  n     mean   color
1     1     4 11 26.66364 #FF0000
2     2     6  7 19.74286 #00FF00
3     3     8 14 15.10000 #0000FF

$check_unbalanced_reps
[1] TRUE

$phrase_selected_check_unbalanced
[1] "The design is unbalanced in repetitions. A correction is applied to the Tukey test."

3) Anova 1 way - Table

$df_table_anova
            Df   Sum Sq   Mean Sq  F value       Pr(>F)
FACTOR       2 824.7846 412.39230 39.69752 4.978919e-09
Residuals   29 301.2626  10.38837       NA           NA

4) Multiple comparation test (Tukey)

$df_tukey_table
  level     mean group
1     4 26.66364     a
2     6 19.74286     b
3     8 15.10000     c

5) Model Error

$df_model_error
  order level  n model_error_var_MSE model_error_sd model_error_se raw_error_se
1     1     4 11            10.38837       3.223099      0.9718008    0.9718008
2     2     6  7            10.38837       3.223099      1.2182168    1.2182168
3     3     8 14            10.38837       3.223099      0.8614094    0.8614094

1) Requeriment - Normaility test - Residuals

$test_residuals_normality

    Shapiro-Wilk normality test

data:  minibase_mod$residuals
W = 0.97065, p-value = 0.5177

2) Requeriment - Homogeneity test - Residuals

$test_residuals_homogeneity

    Bartlett test of homogeneity of variances

data:  residuals by FACTOR
Bartlett's K-squared = 8.3934, df = 2, p-value = 0.01505

3) Estimated variances - Residuals

$df_model_error
  order level  n model_error_var_MSE model_error_sd model_error_se raw_error_se
1     1     4 11            10.38837       3.223099      0.9718008    0.9718008
2     2     6  7            10.38837       3.223099      1.2182168    1.2182168
3     3     8 14            10.38837       3.223099      0.8614094    0.8614094

$df_raw_error
  order level  n raw_error_var raw_error_sd
1     1     4 11     20.338545     4.509828
2     2     6  7      2.112857     1.453567
3     3     8 14      6.553846     2.560048

$phrase_info_errors
[1] "Anova and Tukey use MSE from model."                                                              
[2] "Bartlett use variance from raw error on each level."                                              
[3] "Only if there is homogeneity from raw error variances then is a good idea take desition from MSE."
$df_table_factor_plot001
  order level  n     mean  min  max       sd       var
4     1     4 11 26.66364 21.4 33.9 4.509828 20.338545
6     2     6  7 19.74286 17.8 21.4 1.453567  2.112857
8     3     8 14 15.10000 10.4 19.2 2.560048  6.553846

$df_table_factor_plot002
  order level  n     mean model_error_sd lower_limit upper_limmit   color
4     1     4 11 26.66364       3.223099    23.44054     29.88674 #FF0000
6     2     6  7 19.74286       3.223099    16.51976     22.96596 #00FF00
8     3     8 14 15.10000       3.223099    11.87690     18.32310 #0000FF

$df_table_factor_plot003
  order level  n     mean model_error_se lower_limit upper_limmit   color
4     1     4 11 26.66364      0.9718008    25.69184     27.63544 #FF0000
6     2     6  7 19.74286      1.2182168    18.52464     20.96107 #00FF00
8     3     8 14 15.10000      0.8614094    14.23859     15.96141 #0000FF

$df_table_factor_plot004
  order level  min     mean    Q1 median    Q3  max  n   color
4     1     4 21.4 26.66364 22.80   26.0 30.40 33.9 11 #FF0000
6     2     6 17.8 19.74286 18.65   19.7 21.00 21.4  7 #00FF00
8     3     8 10.4 15.10000 14.40   15.2 16.25 19.2 14 #0000FF

$df_table_factor_plot005
  order level  min     mean    Q1 median    Q3  max  n   color
4     1     4 21.4 26.66364 22.80   26.0 30.40 33.9 11 #FF0000
6     2     6 17.8 19.74286 18.65   19.7 21.00 21.4  7 #00FF00
8     3     8 10.4 15.10000 14.40   15.2 16.25 19.2 14 #0000FF

$df_table_factor_plot006
  order level  min     mean    Q1 median    Q3  max  n   color
4     1     4 21.4 26.66364 22.80   26.0 30.40 33.9 11 #FF0000
6     2     6 17.8 19.74286 18.65   19.7 21.00 21.4  7 #00FF00
8     3     8 10.4 15.10000 14.40   15.2 16.25 19.2 14 #0000FF

$df_table_factor_plot007
  order level  n     mean model_error_se lower_limit upper_limmit   color group
4     1     4 11 26.66364      0.9718008    25.69184     27.63544 #FF0000     a
6     2     6  7 19.74286      1.2182168    18.52464     20.96107 #00FF00     b
8     3     8 14 15.10000      0.8614094    14.23859     15.96141 #0000FF     c

$df_table_residuals_plot001
  order level  n       min          mean      max       var       sd   color
4     1     4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6     2     6  7 -1.942857 -7.943233e-18 1.657143  2.112857 1.453567 #00FF00
8     3     8 14 -4.700000  1.193252e-17 4.100000  6.553846 2.560048 #0000FF

$df_table_residuals_plot002
  order level  n       min          mean      max       var       sd   color
4     1     4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6     2     6  7 -1.942857 -7.943233e-18 1.657143  2.112857 1.453567 #00FF00
8     3     8 14 -4.700000  1.193252e-17 4.100000  6.553846 2.560048 #0000FF

$df_table_residuals_plot003
  order level  n       min          mean      max       var       sd   color
4     1     4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6     2     6  7 -1.942857 -7.943233e-18 1.657143  2.112857 1.453567 #00FF00
8     3     8 14 -4.700000  1.193252e-17 4.100000  6.553846 2.560048 #0000FF

$df_table_residuals_plot004
   variable  n       min          mean      max      var       sd
1 residuals 32 -5.263636 -1.040834e-17 7.236364 9.718148 3.117394
  model_error_var_MSE model_error_sd
1            10.38837       3.223099

$df_table_residuals_plot005
   variable  n       min          mean      max      var       sd
1 residuals 32 -5.263636 -1.040834e-17 7.236364 9.718148 3.117394
  model_error_var_MSE model_error_sd
1            10.38837       3.223099

$df_table_residuals_plot006
  order level  n        min          mean       max       var        sd   color
4     1     4 11 -1.6330981 -2.020559e-17 2.2451573 1.9578196 1.3992211 #FF0000
6     2     6  7 -0.6027917 -2.723816e-18 0.5141459 0.2033869 0.4509843 #00FF00
8     3     8 14 -1.4582240 -1.256150e-18 1.2720678 0.6308833 0.7942816 #0000FF

$df_table_residuals_plot007
  order level  n        min          mean       max       var        sd   color
4     1     4 11 -1.6330981 -2.020559e-17 2.2451573 1.9578196 1.3992211 #FF0000
6     2     6  7 -0.6027917 -2.723816e-18 0.5141459 0.2033869 0.4509843 #00FF00
8     3     8 14 -1.4582240 -1.256150e-18 1.2720678 0.6308833 0.7942816 #0000FF

$df_table_residuals_plot008
  variable  n       min          mean      max       var        sd
1  studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.9672042

$df_table_residuals_plot009
  variable  n       min          mean      max       var        sd
1  studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.9672042

$df_table_residuals_plot010
  variable  n       min          mean      max       var        sd
1  studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.9672042

1) Summary Anova 1 way

$df_summary_anova
               test         aim  variable      p_value alpha_value
1 Shapiro-Wilk test   Normality residuals 5.176650e-01        0.05
2     Bartlett test Homogeneity residuals 1.504518e-02        0.05
3       Anova 1 way        Mean       mpg 4.978919e-09        0.05
        Decision
1 Ho no rejected
2    Ho Rejected
3    Ho Rejected

$phrase_shapiro_selected
[1] "The null hypothesis of normal distribution of residuals is not rejected."

$phrase_bartlett_selected
[1] "The hypothesis of homogeneity of variances (homoscedasticity) is rejected."

$phrase_requeriments_selected
[1] "Not all model assumptions are met, so it is NOT valid to draw conclusions from the ANOVA test."

$phrase_anova_selected
[1] "Regardless of the p-value obtained in ANOVA, it is not valid to draw conclusions."

2) Tukey

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